"We are a nation of immigrants. It's a source of strength and something we can take pride in," he said.

The president also said, "We can't just celebrate this heritage, we have to defend it by fixing our broken immigration system."

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Obama said Democrats and Republicans in the Senate did that two years ago when they passed "a common sense bill" that included a pathway to citizenship.

However, he said Republican leaders in the House of Representatives for nearly two years "have refused to even allow a vote on it."

"In the meantime, I'm going to keep doing everything I can to make our immigration system more just and more fair," Obama said. "It's the right thing to do. And it will make America stronger."

This June marks the second annual U.S. Immigrant Heritage Month, meant to honor the accomplishments and role of immigrants in shaping U.S. history and culture.

According to the U.S. Census Bureau's 2013 American Community Survey, the nation's immigrant population was more than 41 million, or 13 percent of the total population of 316 million.

U.S. immigration population over time, 1850 - 2013

Mexican-born immigrants are the majority, comprising 28 percent of the 41 million total immigrant populations.

Although the number of Mexican immigrants remains the highest in the country, in recent years it has started to decline as a result of recession, improved educational and economic opportunities at home, and tougher border enforcement.

Meanwhile, immigrant groups from India and China, including Hong Kong, but not Taiwan, each account for about 5 percent of the United States' total immigrant population; many moving to the country to work, study or join family members already here.

The Philippines has the fourth highest number of immigrants living in the United States at 4 percent, while residents from Vietnam, El Salvador, Cuba and Korea each make up 3 percent of the immigrant total.

Immigration restrictions

Up until the mid-1960s, immigration restrictions in the United States favored the entry of people from Europe.

However, with the passage of the Immigration and Nationality Act – a law that made it so people would be admitted based on their occupational skills rather than their country of origin – the makeup of most immigrants also changed from Europe to Latin America and Asia.

In 1960, Europeans made up nearly 75 percent of the U.S. immigrant population, but by 2013 that number dwindled to just 11.6 percent. During the same period, immigrants from South and Central America increased from 19-to-54 percent.